Question

claudia purchases a valuable item. the equation below models the value of the item, y, after x years. select the correct statement regarding the parameter 1.03.\\( y = 9400(1.03)^x \\)\
show your work here\
\\(\circ\\) the item depreciates at an annual rate of 3%\
\\(\circ\\) the item loses $3 of value each year\
\\(\circ\\) the item gains $3 of value each year\
\\(\circ\\) the item appreciates at an annual rate of 3%

Explanation:

Step1: Recall exponential growth formula

The standard exponential growth model is $y = a(1+r)^x$, where $a$ is initial value, $r$ is annual growth rate, and $x$ is time in years.

Step2: Compare given formula to model

Given $y = 9400(1.03)^x$, rewrite as $y = 9400(1+0.03)^x$.

Step3: Identify rate and trend

Here, $r=0.03=3\%$. Since $1+r>1$, the value increases (appreciates) annually at 3%.

Answer:

The item appreciates at an annual rate of 3%